Given recent developments in the long-running hunt for dark matter and the difficulty interpreting what this means, it seems like a good juncture to re-up* this:
The history of science is a decision tree. Vertices appear where we must take one or another branching. Sometimes, we take the wrong road for the right reasons.
A good example is the geocentric vs. heliocentric cosmology. The ancient Greeks knew that in many ways it made more sense for the earth to revolve around the sun than vice-versa. Yet they were very clever. Ptolemy and others tested for the signature of the earth’s orbit in the seasonal wobbling in the positions of stars, or parallax. If the earth is moving around the sun, nearby stars should appear to move on the sky as the earth moves from one side of the sun to the other. Try blinking back and forth between your left and right eyes to see this effect, noting how nearby objects appear to move relative to distant ones.
Problem is, Ptolemy did not find the parallax. Quite reasonably, he inferred that the earth stayed put. We know now that this was the wrong branch to choose, but it persisted as the standard world view for many centuries. It turns out that even the nearest stars are so distant that their angular parallax is tiny (the angle of parallax is inversely proportional to distance). Precision sufficient for measuring the parallax was not achieved until the 19th century, by which time astronomers were already convinced it must happen.
Ptolemy was probably aware of this possibility, though it must have seemed quite unreasonable to conjecture at that time that the stars could be so very remote. The fact was that parallax was not observed. Either the earth did not move, or the stars were ridiculously distant. Which sounds more reasonable to you?
So, science took the wrong branch. Once this happened, sociology kicked in. Generation after generation of intelligent scholars confirmed the lack of parallax until the opposing branch seemed so unlikely that it became heretical to even discuss. It is very hard to reverse back up the decision tree and re-assess what seems to be such a firm conclusion. It took the Copernican revolution to return to that ancient decision branch and try the other one.
Cosmology today faces a similar need to take a few steps back on the decision tree. The problem now is the issue of the mass discrepancy, typically attributed to dark matter. When it first became apparent that things didn’t add up when one applied the usual Law of Gravity to the observed dynamics of galaxies, there was a choice. Either lots of matter is present which happens to be dark, or the Law of Gravity has to be amended. Which sounds more reasonable to you?
Having traveled down the road dictated by the Dark Matter decision branch, cosmologists find themselves trapped in a web of circular logic entirely analogous to the famous Ptolemaic epicycles. Not many of them realize it yet, much less admit that this is what is going on. But if you take a few steps back up the decision branch, you find a few attempts to alter the equations of gravity. Most of these failed almost immediately, encouraging cosmologists down the dark matter path just as Ptolemy wisely chose a geocentric cosmology. However, one of these theories is not only consistent with the data, it actually predicts many important new results. This theory is known as MOND (MOdified Newtonian Dynamics). It was introduced in 1983 by Moti Milgrom of the Weizmann Institute in Israel.
MOND accurately describes the effective force law in galaxies based only on the observed stars and gas. What this means is unclear, but it clearly means something! It is conceivable that dark and luminous matter somehow interact to mimic the behavior stipulated by MOND. This is not expected, and requires a lot of epicyclic thinking to arrange. The more straightforward interpretation is that MOND is correct, and we took the wrong branch of the decision tree back in the ’70s.
MOND has dire implications for much modern cosmological thought which has developed symbiotically with dark matter. As yet, no one has succeeded in writing down a theory which encompasses both MOND and General Relativity. This leaves open many questions in cosmology that were thought to be solved, such as the expansion history of the universe. There is nothing a scientist hates to do more than unlearn what was thought to be well established. It is this sociological phenomenon that makes it so difficult to climb back up the decision tree to the faulty branching.
Once one returns and takes the correct branch, the way forward is not necessarily obvious. The host of questions which had been assigned seemingly reasonable explanations along the faulty branch must be addressed anew. And there will always be those incapable of surrendering the old world view irrespective of the evidence.
In my opinion, the new successes of MOND can not occur by accident. They are a strong sign that we are barking up the wrong tree with dark matter. A grander theory encompassing both MOND and General Relativity must exist, even if no one has as yet been clever enough to figure it out (few have tried).
These all combine to make life as a cosmologist interesting. Sometimes it is exciting. Often it is frustrating. Most of the time, “interesting” takes on the meaning implied by the old Chinese curse:
MAY YOU LIVE IN INTERESTING TIMES
Like it or not, we do.
*I wrote this in 2000. I leave it to the reader to decide how much progress has been made since then.
Philip W. Anderson gave the answer to these questions in 1972 in his seminal paper: More is different.
Reality has a hierarchical structure and that automatically imposes limitations to the applicability range of any theory.
There’s no grander theory encompassing both MOND and General Relativity because each one of them has intrinsic limitations.
Naive reductionism: assuming that theories have universal applicability is the underlying blunder, the same mistake made by the people looking for a theory of everything and also by the proponents of string theory.
Emergent irreducible properties (strong emergence) is a reality in complex systems that reductionist mindsets refuse to accept even with strong mathematical results supporting it.
Naive reductionism is exactly like a religion, a very expensive religion by the way wasting social resources in the millions, looking for a fictitious dark matter, or non observable strings, or dark energy… But it’s very well known that pragmatism is a foreign notion in academia, detachment from reality is the norm not the exception.
I suspect we will have to back up to some earlier decision branches, such as the expanding universe hypothesis. Having pointed out previously that is intergalactic space were to expand, the speed of the light crossing it should increase proportionally, in order to remain Constant!
As it is, two metrics are being derived from the speed and spectrum of the same light. Given it is an expanding space and not tired light theory, the speed is still the denominator.
I bring this up, because more evidence of an infinite universe is appearing, as those little red dots appearing by the thousands. Which would be much further galaxies, that can’t be shoehorned in the current model.
https://www.scientificamerican.com/article/jwsts-little-red-dots-offer-astronomers-the-universes-weirdest-puzzle/
As for dark matter, what if the properties our tactile, object oriented senses associate with matter are only part of a larger centripetal dynamic? Basically that mass is an effect of gravity, which extends from the barest bending of the light to black holes. Rather than gravity as a property of mass.
Consider that galaxies are energy radiating out, as structure coalesces in. In which the most basic dynamic would be a synchronization of wave structure.
“I leave it to the reader to decide how much progress has been made since then.”
More have tried than had in 2000.
I have a running list of approached beyond strict MOND paradigm efforts (which deserve their own list one of these days), with linked citations, of the attempts.
My list also includes your own tree illustrating the various approaches (but with print that is too small, I’d love to see a new version in a larger font).
Some only address dark matter phenomena but not dark energy phenomena (including MOND), or only address dark energy phenomena but not dark matter phenomena.
My list isn’t complete, but it is a longer annotated bibliography than I’ve seen anywhere else. https://dispatchesfromturtleisland.blogspot.com/2024/06/a-survey-of-notable-non-mond-modified.html
Alexandre Deur’s papers appeared before the spate of wide binary results in 2023. What does Deur’s gravitational self-interaction have to say about the wide binaries?
Martin Haavinga answered this question further down below in the questions: Deur’s gravitational self-interaction would predict Newtonian behaviour for wide binaries, as well as Newtonian behaviour for other things like the planet 9 phenomenon in the solar system, since there isn’t enough gravitational self-interaction to exhibit MOND behaviour. So these smaller systems provide a ways of distinguishing between MOND and gravitational self-interaction.
Deur’s analysis suggests that you shouldn’t see noticeable non-Newtonian effects in wide binaries (this is me applying his papers, not him himself saying so). https://dispatchesfromturtleisland.blogspot.com/2022/10/wide-binary-star-tests-of-modified.html
This article had me totally fooled. I failed to parse the introduction and then read the article as though it was talking about the present state of affairs, not the state a quarter century ago. A sad testament to how little has changed in standard cosmology, and how slowly science backtracks from a false path.
The biggest indication that this article wasn’t written about today is this sentence
“As yet, no one has succeeded in writing down a theory which encompasses both MOND and General Relativity.”
This may have been true in 2000 but isn’t true in 2024. In the past few years there’s been a proliferation of relativistic MOND theories in the astrophysical literature, such as
New relativistic theory for Modified Newtonian Dynamics
Broader view of bimetric MOND
Consistent cosmological structure formation on all scales in relativistic extensions of MOND
Khronometric theories of modified Newtonian dynamics
and Stacy McGaugh has written a number of blog posts on some of these theories.
Good call. I chose not to edit it at all. Another indication (and how I could date it myself!) is the reference to the then-current state of CMB observations in the “recent” observations.
As an historical note, TeVeS appeared in 2004. That was perhaps the first relativistic theory containing MOND that was not obviously wrong from the outset. Of course it had precursors; Bekenstein outlined RAQUAL already in his 1984 paper with Milgrom. He could never get it to do the right thing for gravitational lensing, much as TeVeS subsequently proved to do the wrong thing for gravitational waves.
This is not a problem one solves overnight.
Would you be so kind as to send me an email. I would like to ask you something about the Tolman articles.
That article will travel through time, and spookily apply in any era…. One possibile part of the story is that GR was a wrong branch. It’s now widely seen as an approximation – and that means wrong. Raphael Bousso: ‘As a matter of principle, the theory is wrong. The seed is there. General relativity cannot be the final word; it can only be an approximation […]’. Sabine Hossenfelder: ‘Most physicists, myself included, think general relativity is only an approximation to a better theory’.
But the experimental results? Physics is full of equivalence – we already know two theories can make very similar predictions. How far this principle goes, we don’t know, but we’ve found no limit to it so far. And GR doesn’t connect to other physics well, while QM connects well everywhere. So GR being wrong – but looking very right – might explain a few things we’re up against now. (The near-proof I mentioned quietly reinforces that idea.)
Once physics has taken a wrong turn, it’s like a toy car that can only go forwards, they used to make ones that would get stuck in the corner of the room. Physics can’t go back easily, partly because of funding, which keeps reinforcing one central view. And the influence of people who have invested a lot of time into it, including those who teach physics.
About emergence making the laws different: a spiral galaxy shows this isn’t what’s happening. The inner areas of the field go by simple laws that we know work across many scales. Then there’s an unexplained border, and the outer areas work differently. That’s not strong emergence, unless the galaxy suddenly becomes irreducibly complex at the borderline.
I have to admit that the loose picture I’ve been looking at, which is still forming in that area (the theory is utterly certain in other areas), is not a million miles from that. But it’s not about a general principle limiting the range of theories, it’s about a specific change to the field, in which very simple mathematics translates between the two regions – ie. MOND. This simplicity of the mathematics that translates between them, referring to one to reach the other, is a major clue.
It is a major clue to the physically obvious – the gravitational effect tracks the geometry of the matter distribution in a disk galaxy. The further out the disk you go, the more the gravitational effect of the constant spherical central mass drops off (as 1/r^2) while the continuing gravitational effect of the disk mass drops off as 1/r. The geometry of the mass distribution is the cause of the observed effect.
This is the same straightforward physical geometry that applies to the electromagnetic radiation and gravitational effects with regard to spherical emitters – the flux of both falls off with the implied surface area at any given radial distance (1/r^2). This isn’t some ground-breaking observation. On the contrary it is a well known fact.
The problem with the theoretical physics community is that it doesn’t give a shit about the facts. It is solely concerned with the extension and defense of the consensus mathematical models that have been handed down like holy writ for the last 100 years. How these blind dogs got appointed to lead the dogsled of the scientific academy is a socio-economic mystery that can best be sorted out by future historians.
For now the task is to restore physicists, those scientists doing actual physical research, to the lead position, with theoretical physicists required to produce mathematical models that track empirically observed physical reality. The current situation based on the assumed primacy of mathematics in determining the nature of physical reality is as untenable as it is unscientific.
Rummaging around in the febrile human imagination, which is where the math toolbox of theoretical physics exists, has never been a good approach to understanding the nature of physical reality. Ptolemy made a useful math model that was nonetheless completely wrong about the nature of physical reality.
Physical reality can be said to be the source of our sense of what it means to be rational. Physical reality is rational. Mathematical abstractions can be said to be the source of our confusion about the nature of physical reality, as the two standard models of theoretical physics heartily attest.
Yes, the geometry is important, and yes, this is accounted for.
I’m not sure what you mean by accounted for. If the geometry gets you to a 1/r relationship, which is what MOND does, then why do you need MOND?
Physicists take geometry into account.
Nevertheless, mass is missing (Newton) or you have to change the law of gravity (MOND).
The pertinent question is – how? How do theoretical physicists account for the geometry? What do you specifically mean? If they can’t get a 1/r relationship at large distances from the central mass then I suspect they are not properly accounting for the geometry.
My guess is that they simply apply Newton’s shell theorem to the geometry of a disk at all radial distances – which would an analytical error. The radius of a sphere generates a spherical shell. The radius of a circular disk generates a circumferential ring of some nominal thickness. As far as I know there is no ring theorem for gravity.
Given the propensity of theorists for mathematical convenience I suspect they just slapped the Newtonian shell theorem inappropriately on the disk and so confirmed a need for “dark matter” that was first attributed to the lack of an expected Keplerian decline.
I could be wrong about that; but simply stating that the geometry is accounted for without an elaboration on how that accounting is achieved does not answer the point raised: the geometry of a disk suggests a 1/r drop off of the flux through the circumference of the disk.
This was a debate that occurred 40 years ago. At first, people were making a spherical approximation, which predicts a Keplerian decline while observed rotation curves remained flat. Then others noted what is said here: the geometry matters, let’s check that. The way to do that is to solve the Poisson equation numerically. The Poisson equation relates the 3D Newtonian gravitational potential to the 3D mass distribution. It can handle arbitrary distributions, including disks. This was of course known at the time, and an analytic solution (Freeman 1970) was already available for razor thin disks. It is noticeably different from the spherical approximation, but not much. Kalnajs (and others) implemented a numerical solution that allowed for a finite thickness disk and made use of the detailed shape of the observed light profile: i.e, the closest we can get to a 3D mass distribution from observations. Kalnajs made the point that disk rotation curve was flat enough that maybe we didn’t need dark matter. This was an uproarious chapter at the IAU 100 Symposium, related in the comments there (these can be found on-line but I’m not gonna look it up because I am already well over my budget on how much time I’m willing to take to explain ancient history.) So when I say we know how to deal with the disk geometry and have done so, I mean we have solved the Poisson equation for the detailed observed distribution of light as projected in 2D and for 3D assuming a disk thickness equal to the average observed for edge-on spirals. This differs from the spherical approximation at the 20% level.
The thing is, every finite mass looks like a point mass if you get far enough out. So the was to check Kalnajs’s assertion was to measure rotation curves much further out. Get far enough out, and even a disk geometry reverts to inverse square. That was an important threshold to address a legitimate concern. That threshold had been a abundantly exceeded with observations of many dozens of galaxies by the mid-80s.
These are details I teach in grad level courses. I appreciate the high level question, but I’m not here to teach a grad level course. When I say we know how to do something, there is a wealth of scholarship behind it, of which the above is the barest outline and yet also far more than I should need to say here on the subject.
It’s not just the stellar parallax issue that caused astronomers to doubt Copernicanism at the beginning of the 17th Century. When the astronomers looked through the first telescopes they saw the stars as disks (what we now call the Airy disk) not unlike the planets that were seen as disks for the first time. Because diffraction in the telescope was not understood, these were thought to represent the real angular sizes of the stars and this led to calculated star sizes that were much larger than the entire Solar System. Christopher R. Graney’s book “Setting Aside All Authority” (University of Notre Dame Press 2015), which includes the first English translations of both Ingoli’s letter to Galileo disputing the Copernican system and Riccioli’s reports on his experiments with falling bodies, covers this topic well and explains why the Tychonic system, with its stationary Earth, orbited by the Sun but with the remaining planets orbiting the Sun was an attractive alternative theory to Copernicanism. Sometimes even the best observations can be misleading.
Sure. This is obviously a super-condenser version of the story: I just wanted to make that very point, that sometimes even the best observations can be misleading.
One of Galileo’s many great contributions was to show how unworkable it was to have a fixed earth in a geocentric cosmology. Many of those arguments are subtle, and not all are correct (tides, comets), but he did the hard work of showing the inconsistencies of geocentrism on its own terms.
In the same vein, I think my most important work is that which shows that the dark matter interpretation really isn’t satisfactory, on its own terms. I feel like the community has chosen to forget or ignore that, preferring a divide-and-conquer approach in which piece A can be explained and piece B can be explained but left unexamined is that the explanations for A and B are self-contradictory. The Tully-Fisher relation and Renzo’s rule/rotation curve diversity, for example – the former pushes one to infer that dark matter dominates disk galaxies at all radii, while the former requires something close to a maximal contribution from stars. We can’t have both at once, but apparently we can if we only worry about one at a time.
Stacy, my comment wasn’t intended as any sort of criticism of your excellent post, but there is always a tendency to look back at at historical missteps with the benefit of hindsight and be surprised that anyone could ever have rejected the heliocentric model of the Solar system; more recent examples I could have quoted include the Shapley-Curtis debate or Einstein introducing the cosmological constant to save his idea of a non-expanding universe. One of the most difficult things for any scientist to do is to put himself/herself in the shoes of a historical figure and blot out all knowledge of what happened later to truly understand why they thought that way.
Indeed!
It is hard not to oversimplify history. Aether is another good example: today it is taught as “Michelson & Morely proved it wasn’t there” when in fact the debate persisted for decades after their experiment with a common theme being that they had excluded some kinds of aether but not others. For a while, a common attitude seems to have been that one of those others would win out.
Hmm, why does that sound familiar?
We need an ether.
To understand light, we need an aether.
To understand the expansion of the universe we need an ether. And we probably need an aether to deduce MOND.
I’m afraid I have to disagree. Physics doesn’t need yet another invisible helper to cover up for the evergreen analytical inadequacies of the theoretical physics community.
Yes, we need an aether. We do not need an electrical field wagging a magnetic field, wagging etc. We do not need a big bang, at least not of the type and TIME described. But we do need a Higgs structure (aether) with mass units locked in position; yet warped by concentrations of energy. We have a universal aether with a background temperature.
Because it sounds like something that is going on in cosmology right now – people still assuming that the cosmological principle holds even though there are anomalies popping up of various anisotropies and inhomogeneities in our universe, larger than the 260/h Mpc limit set by the current proponents of the cosmological principle. People are trying to contort Lambda CDM with bizarre additions like early dark energy in an attempt to solve the Hubble tension which end up making the S8 tension worse in the process, so that they can keep using the FLRW metric.
There have been challenges to the homogeneity scale for as long as I remember. I’m old enough to remember people making up stories about tiger stripes* to explain away what we now recognize as large scale structure, because no way the universe could be inhomogeneous on tens of Mpc scales. That cratered with the addition of redshift information in the first CfA survey, which found the famous stick man galaxy distribution in 1987 I think it was. People were flabergasted: structure on that scale was a total surprise. One of the key things that finally sank Standard (Omega=1) CDM was the observation of excess power on large scales in the early ’90s. The modern 260/h Mpc scale you mention seems to me to be more a choice of how far out we’ve measured it well than a legitimate theoretical expectation.
We’ve been wrong about this over and over and over again, but we (including me) struggle to let go of the Cosmological Principle. It is deeply embedded in the belief system.
—-
*The argument was about the appearance of long, strip-like linear features of galaxies in 2D galaxy counts as projected on the sky. These couldn’t be real (according to the required homogeneity as it was thought of in the 1970s), no matter how obvious they were to the eye. That’s a psychological illusion thanks to evolution, the argument went. It was better to think you saw a tiger lurking in the woods and run away than it was to miss it and get eaten – so much so that we are programmed to see patterns where they aren’t real, just in case. So that [now known to be real] structure you perceive in the sky is just your mind playing tricks on you so you don’t get eaten by a hypothetical predator that you couldn’t possibly outrun if it came to it.
Yes, this argument was made in all seriousness by famous cosmologists with a straight face.
Btw, I meant GR, but not SR, which is certainly right.
Another place where two points are taken onboard separately, which if taken together contradict each other, is on the question of whether the future already exists. QM has random events that are undecided until they happen, but Minkowski spacetime led to a picture in which the entire future is already laid out in every detail. They can’t both be true (unless you only look at the mathematics). With both, people often say ‘that’s just the way it is’, but they can’t both be just the way it is.
Success of MOND is not by accident. It is purely engineered success. And fake theory can be engineered in this way to sound like a successful theory. Multiply 2 ghosts with three demons and subtract the curvature parameter 3/5 and see that result tallies with observation? No?
Ok … Multiply 2.27 ghosts with 3.9 demons and now see? Yes it is better. It only needs further fine tuning.
If the math of MOND works, and it does (but it isn’t at all as easy as you describe), there indeed is a need for an underlying theory to explain why. But do go on rejecting what we see in reality in order to preserve the easier theory.
Yes it is difficult and manipulative math. Everything is possible to be tallied with any other thing with such manipulative math.
You have absolutely no idea what you’re talking about.
By saying “engineered success,” you imply that MOND can be manipulated to explain any observation. That is plainly not so – once you write down a force law, you’re stuck with it; it has to apply to each and every observed system. That is why its success in galaxies is so impressive – each and every galaxy has a different mass distribution and thereby provides a unique test – while its failure in clusters is so troublesome. If one could “engineer success,” there would be no problem in clusters.
Ironically, it is much easier to engineer success for dark matter. One has the freedom to arrange invisible mass however is needed to explain any observation. This was a hard realization I had thirty years ago. That’s how far behind the curve you are. Maybe more with your talk of mystical, invisible entities like demons and ghosts.
When default behavior of minimal thick galactic disk is flat rotation then there is no need of dark matter, demon, ghost or MOND. Law works everywhere. When law has already worked than MOND is just a manipulated solution. Such manipulations work for systematic errors. That’s why such manipulated solutions seem sort of real. they are not. They are just MOND.
Hi Stacy,
Thank you for this post on Decision Trees & Philosophical Blunders. Your post contains:
“Either lots of matter is present which happens to be dark, or the Law of Gravity has to be amended. Which sounds more reasonable to you?”
If we back up the decision tree, then are there really only two branches to choose from? Surely there should be sensible suggestions out there that don’t need any additional mass and don’t modify the Newton/Einstein laws of gravity?
Well, Alexandre Deur has suggested that MOND is simply an effect of gravitational self-interaction that arises from the nonlinear nature of general relativity:
https://dispatchesfromturtleisland.blogspot.com/p/deurs-work-on-gravity-and-related.html
No. This is not a viable option. There may be some third way, like a hybrid model, but the acceleration discrepancy is a real effect that cannot be explained by any theory known to us before its discovery.
Modified inertia is a good option I’d say, because it introduces no new particles or forces. It would be an entirely new physical effect! We have never explored low accelerations that well before MOND anyway, it’s worth the research.
But as a research project, I found Deur’s approach a nice try and although your argument against it is good, the idea that the geometries of the systems matter interests me still. However, next to your argument, Deur’s approach seems to give no EFE, which contradicts two results of Chae, the planet 9 MOND solution and the sednoid anomaly MOND solution.
Yes, modified inertia is intriguing. Where does inertial mass come from, anyway?
While I don’t think there is any plausible chance that the observed behavior can emerge from GR without modification, I am curious how the metric of a gravitationally bound galaxy maps to that of the expanding space time in which it is embedded. We treat these as distinct entities and I’ve never seen anyone do otherwise.
I am trying to derive MOND from the expansion of the universe. But it’s strange. I would expect the opposite. The expansion of the universe would have to contribute to the disruption of galaxies, how centrifugal force does. It is difficult. Unfortunately, we have no object-based explanation for Newtonian gravity. We have this beautiful formula, this law. But we can’t explain it in material terms. That’s why it’s so difficult to modify Newton and derive MOND. In GR, the curvature of space is offered as an explanation for gravitation. That is a start.
By the way: Does anyone know a good material example for the geometric mean. avg=sqrt(a*b)
e.g. dice would be great, something like this
”Where does inertial mass come from anyway?”
My “old man’s” brain wonders why SR doesn’t already answer this question. SR says, for objects in motion distances are shorter along the direction of motion. IMO this is evidence of an interaction between moving matter and spacetime.
My impiricist friends tell me there is no way to prove this physically. So, then I ask, “philosophically… what is the difference between saying that gravitationally bound objects are ‘imbedded’ in the expanding Spacetime”? Or saying, “moving objects alter distances so that they are shorter along the direction of motion.”?
Both ideas assert a fundamental interaction between matter and Spacetime. No?
So, if a moving object alters the spacetime along and ahead of its direction of motion, it requires some physical altercation that changes the direction of motion so that a new matter-Spacetime interaction prevails to overcome this. IMO this postulated matter-Spacetime interaction looks like an origin for inertia.
Furthermore, because gravitational interactions also involve matter-Spacetime interactions it should not be surprising that inertial mass and gravitational mass are equivalent.
Anyway, that’s what I think about. These thoughts added to an expanding universe that weakens the ‘pull’ of gravity between distant bound structures makes me really skeptical of Mach’s Principle. Although, I’ll allow that all motion within such structures must be along geodesics which may leave Mach an opening. But, only inside structures!
The equivalence of inertial mass with gravitational charge is a foundational principle of general relativity. There are flavors of GR in which it falls out explicitly, e.g., Yilmaz’s gravity. But it is basically an assumption.
In GR terms, I guess one could imagine Mach’s principle occurring as a consequence of the space-like surface set up by all the mass everywhere else. Space-like means it is not in causal contact, but it could be a relic background: the shape of space left behind by all that has come before.
One important thing to realize about modified inertia is that it has to be non-local. Everything in GR is local; MOND breaks that piece of the strong equivalence principle by having an external field effect. It makes a difference to the dynamics of a small, low acceleration system if it is influenced by the field of a more massive galaxy or if it is off in the middle of nowhere all by its lonesome.
If one takes Banik’s 16-sigma result over Chae’s and Hernandez’s results, wide binaries would be an argument in favour of Deur’s theory.
I found Chae and Hernandez much more convincing than Banik. Hopefully, Banik comes up with something more solid, or even better, they collectively figure out where the difference lies.
As far as I’m concerned, the paper from Chae et al. on wide binaries, combined with the one from Mistele et al. on the Tully-Fisher relation at large radii from weak lensing, rules out dark matter and leaves MOND as the sole explanation for all gravitation-related oddities we observe.
Personally I’m reserving judgment on the wide binaries at least until something new comes out about the issue.
But the overall trend in astrophysics is clear – every few months there is a new paper which claims to have discovered another anomaly which looks like MOND behaviour where it should have been Newtonian/Einsteinian behaviour. Sooner or later, if this trend continues, these anomalies will pile up until the astrophysics community at large begins to notice these growing anomalies and conclude that maybe the universe isn’t described by general relativity.
I thought the Banik article was terrible:
But the article is the opposite of this and achieves its result from tricky statistics.
There is a big problem with that paper I pointed out here earlier, the model under produces scatter so in order to match the data it needs a much too high density of unresolved multiples, these then increase the expected velocity, and so the model is biased towards theories which under predict velocity, this would include Newton if there are actually MOND like effects in the data.
This is well discussed by Henandez and Chae:
“Since there is a substantial level of unacknowledged noise in the unique observational template being used by Banik et al. (2024), and since the models being tested have to accord with the mean levels of ̃ v values, as the MOND model naturally implies a 20% shift towards larger ̃ v values when compared to a Newtonian model, in the MOND case there is that much less room for including a noisy component in comparison to the Newtonian one. Hence, the lower mean ̃ v values of the Newtonian model allow to better accommodate a noisy component to better fit the unacknowledged level of observational noise present in the fixed template, which appears in the form of a high fraction of hidden tertiaries.“
Hernandez, X., and Kyu-Hyun Chae. 2024. ‘On the Methodological Shortcomings in the Wide Binary Gravity Test of Banik et al. 2024’. arXiv. https://doi.org/10.48550/arXiv.2312.03162.
Dear Prof. McGaugh,
an off-topic question:
What you have reported about BCGs in a comment of a previous post is puzzling: “It seems that BCGs at the centers of clusters appear to share the discrepancy of the clusters of which they are part.”
Is there a paper available, or a link, where one can find more information about it?
Do you plan a blog-post about this topic?
Thank you in advance for your response.
There is a paper on this at https://arxiv.org/abs/2402.12016. I don’t know when I might get around to blogging on it; I have unfinished posts from months ago.
Perhaps Andrew, Stacy or someone could say something about these:
* Deur’s solution predicts and explains a previously unnoticed relationship between the apparent amount of dark matter in an elliptical galaxy and the extent to which the galaxy is not spherical, which other modified gravity and dark matter particle theories do not.
* Deur’s solution predicts and explains a previously unnoticed relationship between the thickness of a disk galaxy and the apparent amount of dark matter in a disk galaxy.
Incidentally, there have been a few theories involving gravitational self-interaction of one kind or another. Roy Britten was a respected biologist, the Wikipedia page doesn’t even mention his gravity theory, but loosely as in Planck scale gravity, he thought gravity arises from something emitted by the mass, which after a while starts to self-interact, leading to 1/r behaviour instead of 1/r^2.
‘The hypothesis is that the agent of gravitational force is propagated as if it were scattered with a mean free path of ≈ 5 kiloparsecs. As a result, the force between moderately distant masses, separated by more than the mean free path, diminishes as the inverse first power of the distance, following diffusion equations, and describes the flat rotation curves of galaxies.’ https://www.pnas.org/doi/full/10.1073/pnas.95.7.3351
I am reticent to criticize things I don’t thoroughly understand. I thoroughly understand the dark matter paradigm – much better than most of its advocates. I do not have that level of understanding of Duer’s approach. I did look at it one point, and it seemed unlikely to bear fruit, so I didn’t bother to learn more. This is, of course, how most people approach MOND. There is too little time to dig deep into every rabbit hole.
What I can say, empirically, is that a distance scale is not relevant to the problem. Switching to a 1/r effect at some fixed length scale like 5 kpc does not work. I showed that explicitly in papers in 1998 and 2004. Any theory that relies on such an effect may be immediately discarded.
Should you face a dull, rainy day and have some found time, there is a full annotated hyperlinked 21 paper bibliography of Deur’s gravitational work (some with co-authors) including a few related papers by others, together with introductory materials (heavily borrowing from one of his power point presentations) explaining the basic concepts of his approach at https://dispatchesfromturtleisland.blogspot.com/p/deurs-work-on-gravity-and-related.html
You could cover this detailed and nuts and bolts summary and read one or two of the key papers in an hour. You could be one of the most knowledgable people on the planet about this approach in two or three days of study.
Some of the particularly notable features of it are that it: (1) replicates MOND in its domain of applicability (with a particular unique interpolation function implied), (2) has the widest domain of applicability possible (including CMB, the evolution of cosmic structure, clusters, and the Bullet cluster), (3) solves the conservation of energy issue associated with dark energy phenomena, (4) simultaneously addresses dark matter phenomena and dark energy phenomena (which also explains the “cosmic coincidence” problem), (5) is natively relativistic and In strong fields, it is GR as conventionally applied (hence the theory lacks the theoretical/technical pathologies of lots of modified gravity theories), (6) doesn’t introduce new particles or fields, indeed, it actually has one less observationally determined physical constant since it doesn’t have a cosmological constant, and (7) it has no free parameters or wiggle room (in principle, anyway).
The expanded domain of applicability relative to MOND is largely achieved by considering how the geometry of the mass distribution impacts gravitational interactions in very weak fields. The math draws heavily on QCD with QCD mathematical concepts applied by analogy (his day job is as a QCD HEP experimentalist and phenomenologist). The effects are absent in perfectly spherically symmetrical systems.
He claims that his approach is derived from gravitational field self-interaction analyzed non-perturbatively, in straight classical GR without a cosmological constant (although it is much more intuitive formulated in the context of gravitons in a quantum gravity theory). In principle, it should be possible to derive the MOND a(0) constant from Newton’s constant in his approach, although he doesn’t, in practice, make this calculation. But even if he is actually modifying GR in some subtle way (e.g. by adding in a version of the MOND constant determined, in practice, by observation), if it works, who cares?
It really doesn’t. MOND has effects in wide binaries and the outer solar system that Deur’s theory can’t replicate. But then again, the wide binaries experiment was performed after Deur’s theory came out, and I’m not sure if Deur even is aware of the “planet nine” anomaly.
Sure. But it replicates MOND in the circumstances where it has been observationally confirmed (viewing wide binaries as a still open question).
Also worth noting that Deur is not relying on GEM effects in GR which many papers have attempted to do in order to reproduce MOND without success.
For the decision tree a very important fact has been discussed. That Ptolemy just failed to find the parallax. Only because it was no idea that parallax had to be too low because there was no idea that stars are too far away.
Now same thing applies to dark matter. Gravitational Lensing is giving the “suggestion” of dark matter only because so far there is no idea that galaxies are too far away than the standard or “scientifically accepted” distances. My estimate is that galaxy officially at 13 billion years light travel distance (i.e. one of the most distant visible galaxies) is located at (light travel) distance of about 182 billion light years.
That is my estimate based on other reasons. However, one better way to find the correct distance should be to see the gravitational lensing. The true distance is one where gravitational lensing no more suggests dark matter. May be that would be around 65 billion light years (light travel) distance. But who cares? Scientists are not doing what they should do.
I thought the same, it’s not a distance scale, it’s when GM/r^2 = a0, for whatever reason. But the loose similarity was interesting, and that kind of picture has some advantages, given the increasing variation in the details we’re getting. For instance, there seems to be an effect relating to the shape of the galaxy, including ellipticals – as you say, the shape of the Newtonian field has been accounted for, but there’s something else on top of that, with a directional aspect, and it’s not DM.
It’s a simple case of electro-chemical processes in the body of biological observer. Photons hit the retina and cascade begins. Yes, evolution could have come up with a halting mechanism which would under certain conditions stop it. And it probably has. Only those mutations proved less successful.
So chain reactions continue down the entropy dictated path. We reach conclusions. We make decisions. Even when input is crappy, coarse, distorted. But what ‘tiger stripes’ fail to point out is; even when input is inferred. Circumstantial.
With some training in self control we can not act on decisions made, that’s the best we can do. With that in mind, apply some almighty statistical analysis on trait sets and nurtured behavior characteristics of scientific population, add socio-economic changes science started to feel exponentially with industrial revolution$ and what you see is what you are getting.
Both HEP and cosmology need their Gödel moments (one, actually, but let’s keep it simple). Where we realise we’re not going to solve either. Unfortunately, they’d be unprovable and we’ve missed the boat anyway.
You are correct Martin, scientific progress is super useful and one of the best funs a human being can have. As long as one is aware of its limitations.
# One minor possible advantage being that it portraits the setting better; our ancestors having to venture out into grass/bush land due to climate change and population pressure. Plus I find the thought of a lioness laying ambush in a bush far more terrifying than a tiger trying to climb up a tree.
$ Could be the person who invented the wheel for one tribe was made the king and given all the virgins but it also could be that the inventor in another tribe was staked, roasted and eaten. What industrial revolution brought in spades is realisation science can be profitable. Even better, it is profitable indirectly which also means scientists are controllable easier.
I like your reference to Godel. It’s indeed very good to realize the limits of science very well. Godel’s theorems are technical limits, and those need to be respected. In the case of Stacy’s goal to convince scientific mainstream of that MOND is worth investigating, the limits encountered are sociological.
My reaction was unfortunately led by a little anger (scientific progress is strongly correlated but not at all synonymous with acceptance in the scientific community), anger that you advised Stacy to just go on with science without caring about the rest of the community, especially because you almost suggested that the care for those people had no real use. It was a harsh treatment where a careful note would not have angered me, like: Stacy, after all the work you and others did, I wonder how much value there is in convincing the people that have not yet been convinced. I’m sorry I initially misunderstood you a lot.
(it’s Maarten, peculiarity of dutch language)
It’s clear enough that there are very simple laws underneath the universe. We’re just trying to find them. Anything else about the identity of science, a lot of physicists will tend to ignore. We know there are very simple laws that apply across many orders of magnitude, but to go further now, with the new data we’re getting, we need a picture of what’s going on underneath them. And there are good new clues – the RAR in clusters only became distinct this year, before that it was a possibility. So it’s just a puzzle, like many other puzzles. Stefan said does anyone know of a physical situation in which the geometric mean is used, and I’ve thought the same thing, it’s a good question. There aren’t many, and MOND can be expressed in a lot of different ways. One is that any acceleration beyond a0 is simply boosted by r/rM, so the further out you go, the more accelerations are boosted. rM is the MOND radius (GM/a0)^1/2. That looks a lot more like something is going on – to do with radial aspects of the field, but depending on the mass as well.
OK, this has been a mostly interesting thread with a lot of good discussion, but there has also been a spike in bad behavior from multiple sources (including one apparently using a pseudonym to try to duck a well-earned ban from several years ago) so comments are now closed.